>>11933006>thoughts on the godel incompleteness theorem?>there are computationally undecidable statement in arithmeticSince we have computers now and the Halting problem result is not too hard to understand, today Gödel 1 doesn't really have the same impact on people. It's been absorbed into common knowledge to a good degree.

>arithmetic can't formalize it's consistencyIt's somewhat superseded by Tarski's result and there's several proves of consistency of Peano arithmetic in other systems (Gentzens ordinals, modal operators in provability logic with alternative formalizations of Con_T, self-consistent arithmetic-like theories with infinite axiom systems, and weak self-consistent-proving arithmetics if you want to count them too). Gödel 2 is thus somewhat of a party trick and no more, imho.

>>11933006>I've always had this hunch it may be the solution to unsolved mathematical problems such as the millennium prize problemsA Riemann hypothesis disprove is arithmetical (RH is Pi_1 I think) and some of the Millenium Problems like Navier Stokes existence-uniqueness are pure math memes to begin with anyway.

There's academic papers on potential undecidability of PvNP if you're interested.